ON THE TIME-DEPENDENT LAGRANGIAN APPROACH IN QUANTUM-CHEMISTRY

We formulate the time-dependent variational principle in the form of t he Euler-Lagrange equations, and demonstrate that standard variational as well as nonvariational wave functions may be obtained from these. We also demonstrate how inherently real expectation values of Hermitia n operators can he constructed fur nonvariational wave functions by us ing the time-dependent Hellmann-Feynman theorem which, in turn, is a s imple consequence of the Euler-Lagrange equations. The procedure is il lustrated by derivation of time-dependent Hartree-Fock and of time-dep endent coupled cluster theory. Finally we give the fundamental equatio ns for molecular dynamics within semiclassical electron nuclear dynami cs (END) with a classical description of the nuclei and coupled cluste r description of the electrons. (C) 1998 American Institute of Physics .